Let the function $f(x)=2 x^2-$ logex, $x>0$, be decreasing in (0, a) and increasing in (a, 4). A tangent to the parabola $y^2=4 a x$ at a point $P$ on it passes through the point $(8 a, 8 a-1)$ but does not pass through the point $\left(-\frac{1}{a}, 0\right)$. If the equation of the normal at $P$ is $\frac{x}{\alpha}+\frac{y}{\beta}=1$, then $\alpha+\beta$ is equal to -